Chemical Process Design and Integration
Chemical Process Design and Integration
Robin Smith
Centre for Process Integration,
School of Chemical Engineering and Analytical Science,
University of Manchester.
Chemical Process Design and Integration
Chemical Process Design and Integration
Robin Smith
Centre for Process Integration,
School of Chemical Engineering and Analytical Science,
University of Manchester.
Previous edition published by McGraw Hill
Copyright 2005
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Library of Congress Cataloging-in-Publication Data
Smith, R. (Robin)
Chemical process design and integration / Robin Smith.
p. cm.
Includes bibliographical references and index.
ISBN 0-471-48680-9 (HB) (acid-free paper) – ISBN 0-471-48681-7 (PB) (pbk. :
acid-free paper)
1. Chemical processes. I. Title.
TP155.7.S573 2005
660′ .2812 – dc22
2004014695
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN 0-471-48680-9 (cloth)
0-471-48681-7 (paper)
Typeset in 10/12pt Times by Laserwords Private Limited, Chennai, India
Printed and bound in Spain by Grafos, Barcelona
This book is printed on acid-free paper responsibly manufactured from sustainable forestry
in which at least two trees are planted for each one used for paper production.
To my family
Contents
Preface
xiii
Acknowledgements
Nomenclature
Chapter 1 The Nature of Chemical Process
Design and Integration
1.1 Chemical Products
1.2 Formulation of the Design Problem
1.3 Chemical Process Design and
Integration
1.4 The Hierarchy of Chemical Process
Design and Integration
1.5 Continuous and Batch Processes
1.6 New Design and Retrofit
1.7 Approaches to Chemical Process
Design and Integration
1.8 Process Control
1.9 The Nature of Chemical Process
Design and Integration – Summary
References
Chapter 2 Process Economics
2.1
2.2
2.3
2.4
2.5
2.6
2.7
The Role of Process Economics
Capital Cost for New Design
Capital Cost for Retrofit
Annualized Capital Cost
Operating Cost
Simple Economic Criteria
Project Cash Flow and Economic
Evaluation
2.8 Investment Criteria
2.9 Process Economics – Summary
2.10 Exercises
References
Chapter 3 Optimization
3.1
3.2
3.3
3.4
3.5
Objective Functions
Single-variable Optimization
Multivariable Optimization
Constrained Optimization
Linear Programming
xv
xvii
1
1
3
4
5
9
10
11
13
14
14
17
17
17
23
24
25
28
29
30
31
32
33
35
35
37
38
42
43
3.6
3.7
3.8
3.9
Nonlinear Programming
Profile Optimization
Structural Optimization
Solution of Equations
using Optimization
3.10 The Search for Global
Optimality
3.11 Summary – Optimization
3.12 Exercises
References
Chapter 4 Thermodynamic Properties and
Phase Equilibrium
4.1 Equations of State
4.2 Phase Equilibrium for Single
Components
4.3 Fugacity and Phase Equilibrium
4.4 Vapor–Liquid Equilibrium
4.5 Vapor–Liquid Equilibrium Based on
Activity Coefficient Models
4.6 Vapor–Liquid Equilibrium Based on
Equations of State
4.7 Calculation of Vapor–Liquid
Equilibrium
4.8 Liquid–Liquid Equilibrium
4.9 Liquid–Liquid Equilibrium Activity
Coefficient Models
4.10 Calculation of Liquid–Liquid
Equilibrium
4.11 Calculation of Enthalpy
4.12 Calculation of Entropy
4.13 Phase Equilibrium and Thermodynamic
Properties – Summary
4.14 Exercises
References
Chapter 5 Choice of Reactor I – Reactor
Performance
5.1
5.2
5.3
5.4
5.5
5.6
5.7
Reaction Path
Types of Reaction Systems
Reactor Performance
Rate of Reaction
Idealized Reactor Models
Choice of Idealized Reactor Model
Choice of Reactor Performance
45
46
48
52
53
54
54
56
57
57
59
60
60
62
64
64
70
71
71
72
74
74
74
76
77
77
78
81
82
83
90
94
viii
Contents
5.8 Choice of Reactor
Performance – Summary
5.9 Exercises
References
Chapter 6 Choice of Reactor II - Reactor
Conditions
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
Reaction Equilibrium
Reactor Temperature
Reactor Pressure
Reactor Phase
Reactor Concentration
Biochemical Reactions
Catalysts
Choice of Reactor
Conditions – Summary
6.9 Exercises
References
Chapter 7 Choice of Reactor III – Reactor
Configuration
7.1 Temperature Control
7.2 Catalyst Degradation
7.3 Gas–Liquid and Liquid–Liquid
Reactors
7.4 Reactor Configuration
7.5 Reactor Configuration for
Heterogeneous Solid-Catalyzed
Reactions
7.6 Reactor Configuration from
Optimization of a Superstructure
7.7 Choice of Reactor
Configuration – Summary
7.8 Exercises
References
Chapter 8 Choice of Separator for
Heterogeneous Mixtures
8.1 Homogeneous and Heterogeneous
Separation
8.2 Settling and Sedimentation
8.3 Inertial and Centrifugal Separation
8.4 Electrostatic Precipitation
8.5 Filtration
8.6 Scrubbing
8.7 Flotation
8.8 Drying
8.9 Separation of Heterogeneous
Mixtures – Summary
8.10 Exercises
References
94
95
96
97
97
100
107
108
109
114
114
117
118
120
121
121
123
124
127
133
133
139
139
140
143
143
143
147
149
150
151
152
153
154
154
155
Chapter 9 Choice of Separator for
Homogeneous Fluid Mixtures
I – Distillation
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
Single-Stage Separation
Distillation
Binary Distillation
Total and Minimum Reflux
Conditions for Multicomponent
Mixtures
Finite Reflux Conditions for
Multicomponent Mixtures
Choice of Operating Conditions
Limitations of Distillation
Separation of Homogeneous Fluid
Mixtures by Distillation – Summary
Exercises
References
Chapter 10 Choice of Separator for
Homogeneous Fluid Mixtures
II – Other Methods
10.1
10.2
10.3
10.4
10.5
10.6
10.7
Absorption and Stripping
Liquid–Liquid Extraction
Adsorption
Membranes
Crystallization
Evaporation
Separation of Homogeneous Fluid
Mixtures by Other
Methods – Summary
10.8 Exercises
References
Chapter 11 Distillation Sequencing
11.1 Distillation Sequencing Using
Simple Columns
11.2 Practical Constraints Restricting
Options
11.3 Choice of Sequence for Simple
Nonintegrated Distillation Columns
11.4 Distillation Sequencing Using
Columns With More Than Two
Products
11.5 Distillation Sequencing Using
Thermal Coupling
11.6 Retrofit of Distillation Sequences
11.7 Crude Oil Distillation
11.8 Distillation Sequencing Using
Optimization of a Superstructure
11.9 Distillation Sequencing – Summary
11.10 Exercises
References
157
157
157
160
163
170
175
176
177
178
179
181
181
184
189
193
203
206
208
209
209
211
211
211
212
217
220
224
225
228
230
231
232
Contents
Chapter 12 Distillation Sequencing for
Azeotropic Distillation
12.1 Azeotropic Systems
12.2 Change in Pressure
12.3 Representation of Azeotropic
Distillation
12.4 Distillation at Total Reflux
Conditions
12.5 Distillation at Minimum Reflux
Conditions
12.6 Distillation at Finite Reflux
Conditions
12.7 Distillation Sequencing Using an
Entrainer
12.8 Heterogeneous Azeotropic
Distillation
12.9 Entrainer Selection
12.10 Trade-offs in Azeotropic Distillation
12.11 Multicomponent Systems
12.12 Membrane Separation
12.13 Distillation Sequencing for
Azeotropic Distillation – Summary
12.14 Exercises
References
Chapter 13 Reaction, Separation and Recycle
Systems for Continuous Processes
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
13.10
13.11
The Function of Process Recycles
Recycles with Purges
Pumping and Compression
Simulation of Recycles
The Process Yield
Optimization of Reactor Conversion
Optimization of Processes Involving
a Purge
Hybrid Reaction and Separation
Feed, Product and Intermediate
Storage
Reaction, Separation and Recycle
Systems for Continuous
Processes – Summary
Exercises
References
Chapter 14 Reaction, Separation and Recycle
Systems for Batch Processes
14.1
14.2
14.3
14.4
14.5
Batch Processes
Batch Reactors
Batch Separation Processes
Gantt Charts
Production Schedules for Single
Products
235
235
235
236
238
242
243
14.6 Production Schedules for Multiple
Products
14.7 Equipment Cleaning and Material
Transfer
14.8 Synthesis of Reaction and
Separation Systems for Batch
Processes
14.9 Optimization of Batch Processes
14.10 Storage in Batch Processes
14.11 Reaction and Separation Systems for
Batch Processes – Summary
14.12 Exercises
References
ix
305
306
307
311
312
313
313
315
246
251
253
255
255
255
256
257
258
259
259
264
267
276
280
281
283
284
286
288
289
290
291
291
291
297
303
304
Chapter 15 Heat Exchanger Networks
I – Heat Transfer Equipment
15.1 Overall Heat Transfer Coefficients
15.2 Heat Transfer Coefficients and
Pressure Drops for Shell-and-Tube
Heat Exchangers
15.3 Temperature Differences in
Shell-and-Tube Heat Exchangers
15.4 Allocation of Fluids in
Shell-and-Tube Heat Exchangers
15.5 Extended Surface Tubes
15.6 Retrofit of Heat Exchangers
15.7 Condensers
15.8 Reboilers and Vaporizers
15.9 Other Types of Heat Exchange
Equipment
15.10 Fired Heaters
15.11 Heat Transfer
Equipment – Summary
15.12 Exercises
References
Chapter 16 Heat Exchanger Networks
II – Energy Targets
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
16.10
16.11
Composite Curves
The Heat Recovery Pinch
Threshold Problems
The Problem Table Algorithm
Nonglobal Minimum Temperature
Differences
Process Constraints
Utility Selection
Furnaces
Cogeneration (Combined Heat and
Power Generation)
Integration Of Heat Pumps
Heat Exchanger Network Energy
Targets – Summary
317
317
319
324
329
332
333
337
342
346
348
354
354
356
357
357
361
364
365
370
370
372
374
376
381
383
x
Contents
16.12 Exercises
References
Chapter 17 Heat Exchanger Networks
III – Capital and Total Cost
Targets
17.1
17.2
17.3
17.4
17.5
17.6
Number of Heat Exchange Units
Heat Exchange Area Targets
Number-of-shells Target
Capital Cost Targets
Total Cost Targets
Heat Exchanger Network and
Utilities Capital and Total
Costs – Summary
17.7 Exercises
References
Chapter 18 Heat Exchanger Networks
IV – Network Design
18.1
18.2
18.3
18.4
18.5
18.6
18.7
18.8
18.9
18.10
18.11
The Pinch Design Method
Design for Threshold Problems
Stream Splitting
Design for Multiple Pinches
Remaining Problem Analysis
Network Optimization
The Superstructure Approach to
Heat Exchanger Network Design
Retrofit of Heat Exchanger
Networks
Addition of New Heat Transfer Area
in Retrofit
Heat Exchanger Network
Design – Summary
Exercises
References
Chapter 19 Heat Exchanger Networks
V – Stream Data
19.1 Process Changes for Heat
Integration
19.2 The Trade-Offs Between Process
Changes, Utility Selection, Energy
Cost and Capital Cost
19.3 Data Extraction
19.4 Heat Exchanger Network Stream
Data – Summary
19.5 Exercises
References
383
385
387
387
388
392
393
395
395
396
397
399
399
404
405
408
411
413
416
419
424
425
425
428
429
429
429
430
437
437
438
Chapter 20 Heat Integration of Reactors
20.1 The Heat Integration Characteristics
of Reactors
20.2 Appropriate Placement of Reactors
20.3 Use of the Grand Composite Curve
for Heat Integration of Reactors
20.4 Evolving Reactor Design to Improve
Heat Integration
20.5 Heat Integration of
Reactors – Summary
Reference
Chapter 21 Heat Integration of Distillation
Columns
21.1 The Heat Integration Characteristics
of Distillation
21.2 The Appropriate Placement of
Distillation
21.3 Use of the Grand Composite Curve
for Heat Integration of Distillation
21.4 Evolving the Design of Simple
Distillation Columns to Improve
Heat Integration
21.5 Heat Pumping in Distillation
21.6 Capital Cost Considerations
21.7 Heat Integration Characteristics of
Distillation Sequences
21.8 Heat-integrated Distillation
Sequences Based on the
Optimization of a Superstructure
21.9 Heat Integration of Distillation
Columns – Summary
21.10 Exercises
References
Chapter 22 Heat Integration of Evaporators
and Dryers
22.1 The Heat Integration Characteristics
of Evaporators
22.2 Appropriate Placement of
Evaporators
22.3 Evolving Evaporator Design to
Improve Heat Integration
22.4 The Heat Integration Characteristics
of Dryers
22.5 Evolving Dryer Design to Improve
Heat Integration
22.6 Heat Integration of Evaporators and
Dryers – Summary
439
439
441
442
443
444
444
445
445
445
446
447
449
449
450
454
455
456
457
459
459
459
459
459
460
461
Contents
22.7 Exercises
References
Chapter 23 Steam Systems and Cogeneration
23.1
23.2
23.3
23.4
23.5
23.6
23.7
23.8
23.9
23.10
23.11
23.12
23.13
23.14
462
463
465
Boiler Feedwater Treatment
Steam Boilers
Steam Turbines
Gas Turbines
Steam System Configuration
Steam and Power Balances
Site Composite Curves
Cogeneration Targets
Optimization of Steam Levels
Site Power-to-heat Ratio
Optimizing Steam Systems
Steam Costs
Choice of Driver
Steam Systems and
Cogeneration – Summary
23.15 Exercises
References
466
468
471
477
482
484
487
490
493
496
498
502
506
Chapter 24 Cooling and Refrigeration Systems
513
24.1 Cooling Systems
24.2 Recirculating Cooling Water
Systems
24.3 Targeting Minimum Cooling Water
Flowrate
24.4 Design of Cooling Water Networks
24.5 Retrofit of Cooling Water Systems
24.6 Refrigeration Cycles
24.7 Process Expanders
24.8 Choice of Refrigerant for
Compression Refrigeration
24.9 Targeting Refrigeration Power for
Compression Refrigeration
24.10 Heat Integration of Compression
Refrigeration Processes
24.11 Mixed Refrigerants for Compression
Refrigeration
24.12 Absorption Refrigeration
24.13 Indirect Refrigeration
24.14 Cooling Water and Refrigeration
Systems – Summary
24.15 Exercises
References
Chapter 25 Environmental Design for
Atmospheric Emissions
25.1 Atmospheric Pollution
507
508
510
513
513
516
518
524
526
530
532
535
539
542
544
546
546
547
549
551
551
25.2 Sources of Atmospheric Pollution
25.3 Control of Solid Particulate
Emissions to Atmosphere
25.4 Control of VOC Emissions to
Atmosphere
25.5 Control of Sulfur Emissions
25.6 Control of Oxides of Nitrogen
Emissions
25.7 Control of Combustion Emissions
25.8 Atmospheric Dispersion
25.9 Environmental Design for
Atmospheric Emissions – Summary
25.10 Exercises
References
Chapter 26 Water System Design
26.1
26.2
26.3
26.4
26.5
26.6
26.7
26.8
26.9
26.10
26.11
26.12
26.13
26.14
26.15
26.16
Aqueous Contamination
Primary Treatment Processes
Biological Treatment Processes
Tertiary Treatment Processes
Water Use
Targeting Maximum Water Reuse
for Single Contaminants
Design for Maximum Water Reuse
for Single Contaminants
Targeting and Design for Maximum
Water Reuse Based on Optimization
of a Superstructure
Process Changes for Reduced Water
Consumption
Targeting Minimum Wastewater
Treatment Flowrate for Single
Contaminants
Design for Minimum Wastewater
Treatment Flowrate for Single
Contaminants
Regeneration of Wastewater
Targeting and Design for Effluent
Treatment and Regeneration Based
on Optimization of a Superstructure
Data Extraction
Water System Design – Summary
Exercises
References
Chapter 27 Inherent Safety
27.1
27.2
27.3
27.4
Fire
Explosion
Toxic Release
Intensification of Hazardous
Materials
xi
552
553
554
565
569
573
574
575
576
579
581
583
585
588
591
593
594
596
604
606
607
610
613
616
617
620
620
623
625
625
626
627
628
xii
Contents
27.5 Attenuation of Hazardous Materials
27.6 Quantitative Measures of Inherent
Safety
27.7 Inherent Safety – Summary
27.8 Exercises
References
Chapter 28 Clean Process Technology
28.1 Sources of Waste from Chemical
Production
28.2 Clean Process Technology for
Chemical Reactors
28.3 Clean Process Technology for
Separation and Recycle Systems
28.4 Clean Process Technology for
Process Operations
28.5 Clean Process Technology for
Utility Systems
28.6 Trading off Clean Process
Technology Options
28.7 Life Cycle Analysis
28.8 Clean Process Technology –
Summary
28.9 Exercises
References
Chapter 29 Overall Strategy for Chemical
Process Design and Integration
29.1 Objectives
29.2 The Hierarchy
29.3 The Final Design
B.2 Centrifugal Compressors
B.3 Staged Compression
658
659
Appendix C Heat Transfer Coefficients and
Pressure Drop in Shell-and-tube
Heat Exchangers
661
630
631
632
632
633
C.1 Pressure Drop and Heat Transfer
Correlations for the Tube-Side
C.2 Pressure Drop and Heat Transfer
Correlations for the Shell-Side
References
635
635
662
666
636
637
Appendix D The Maximum Thermal
Effectiveness for 1–2
Shell-and-tube Heat Exchangers
667
Appendix E Expression for the Minimum
Number of 1–2 Shell-and-tube
Heat Exchangers for a Given Unit
669
Appendix F Algorithm for the Heat Exchanger
Network Area Target
671
Appendix G Algorithm for the Heat Exchanger
Network Number of Shells Target
673
G.1 Minimum Area Target for Networks
of 1–2 Shells
References
674
677
642
643
644
645
646
646
647
649
649
649
651
Appendix A Annualization of Capital Cost
653
Appendix B Gas Compression
655
Appendix H Algorithm for Heat Exchanger
Network Capital Cost Targets
Index
B.1 Reciprocating Compressors
661
655
677
679
Preface
This book deals with the design and integration of chemical
processes, emphasizing the conceptual issues that are
fundamental to the creation of the process. Chemical
process design requires the selection of a series of
processing steps and their integration to form a complete
manufacturing system. The text emphasizes both the design
and selection of the steps as individual operations and their
integration to form an efficient process. Also, the process
will normally operate as part of an integrated manufacturing
site consisting of a number of processes serviced by a
common utility system. The design of utility systems has
been dealt with so that the interactions between processes
and the utility system and the interactions between different
processes through the utility system can be exploited to
maximize the performance of the site as a whole. Thus,
the text integrates equipment, process and utility system
design.
Chemical processing should form part of a sustainable
industrial activity. For chemical processing, this means
that processes should use raw materials as efficiently as is
economic and practicable, both to prevent the production
of waste that can be environmentally harmful and to
preserve the reserves of raw materials as much as possible.
Processes should use as little energy as is economic and
practicable, both to prevent the buildup of carbon dioxide
in the atmosphere from burning fossil fuels and to preserve
reserves of fossil fuels. Water must also be consumed in
sustainable quantities that do not cause deterioration in the
quality of the water source and the long-term quantity of the
reserves. Aqueous and atmospheric emissions must not be
environmentally harmful, and solid waste to landfill must
be avoided. Finally, all aspects of chemical processing must
feature good health and safety practice.
It is important for the designer to understand the
limitations of the methods used in chemical process design.
The best way to understand the limitations is to understand
the derivations of the equations used and the assumptions
on which the equations are based. Where practical, the
derivation of the design equations has been included in
the text.
The book is intended to provide a practical guide to
chemical process design and integration for undergraduate
and postgraduate students of chemical engineering, practicing process designers and chemical engineers and applied
chemists working in process development. For undergraduate studies, the text assumes basic knowledge of material and energy balances, fluid mechanics, heat and mass
transfer phenomena and thermodynamics, together with
basic spreadsheeting skills. Examples have been included
throughout the text. Most of these examples do not require
specialist software and can be solved using spreadsheet software. Finally, a number of exercises have been added at
the end of each chapter to allow the reader to practice the
calculation procedures.
Robin Smith
Acknowledgements
The author would like to express gratitude to a number
of people who have helped in the preparation and have
reviewed parts of the text.
From The University of Manchester: Prof Peter Heggs,
Prof Ferda Mavituna, Megan Jobson, Nan Zhang, Constantinos Theodoropoulos, Jin-Kuk Kim, Kah Loong Choong,
Dhaval Dave, Frank Del Nogal, Ramona Dragomir, Sungwon
Hwang, Santosh Jain, Boondarik Leewongtanawit, Guilian Liu, Vikas Rastogi, Clemente Rodriguez, Ramagopal
Uppaluri, Priti Vanage, Pertar Verbanov, Jiaona Wang, Wenling Zhang.
From Alias, UK: David Lott.
From AspenTech: Ian Moore, Eric Petela, Ian Sinclair,
Oliver Wahnschafft.
From CANMET, Canada: Alberto Alva-Argaez, Abdelaziz Hammache, Luciana Savulescu, Mikhail Sorin.
From DuPont Taiwan: Janice Kuo.
From Monash University, Australia: David Brennan,
Andrew Hoadley.
From UOP, Des Plaines, USA: David Hamm, Greg
Maher.
Gratitude is also expressed to Simon Perry, Gareth
Maguire, Victoria Woods and Mathew Smith for help in
the preparation of the figures.
Finally, gratitude is expressed to all of the member
companies of the Process Integration Research Consortium,
both past and present. Their support has made a considerable
contribution to research in the area, and hence to this text.
Nomenclature
a
A
Activity (–), or
constant in cubic equation of state
(N·m4 ·kmol−2 ), or
correlating coefficient (units depend on
application), or
cost law coefficient ($), or
order of reaction (–)
Absorption factor in absorption (–), or
annual cash flow ($), or
constant in vapor pressure correlation
(N·m−2 , bar), or
heat exchanger area (m2 )
ACF
Annual cash flow ($·y−1 )
ADCF
Annual discounted cash flow ($·y−1 )
AI
Heat transfer area on the inside of tubes
(m2 ), or
interfacial area (m2 , m2 ·m−3 )
BOD
Biological oxygen demand (kg·m−3 ,
mg·l−1 )
c
Capital cost law coefficient (–), or
order of reaction (–)
cD
Drag coefficient (–)
cF
Fanning friction factor (–)
cL
Loss coefficient for pipe or pipe fitting
(–)
C
Concentration (kg·m−3 , kmol·m−3 ,
ppm), or
constant in vapor pressure correlation
(K), or
number of components (separate
systems) in network design (–)
CB
Base capital cost of equipment ($)
Ce
Environmental discharge concentration
(ppm)
AM
Membrane area (m2 )
ANETWORK
Heat exchanger network area (m2 )
CE
AO
Heat transfer area on the outside of
tubes (m2 )
Equipment capital cost ($), or
unit cost of energy ($·kW−1 , $·MW−1 )
CF
Heat exchanger area for an individual
shell (m2 )
Fixed capital cost of complete
installation ($)
CP
Specific heat capacity at constant
pressure (kJ·kg−1 ·K−1 ,
kJ·kmol−1 ·K−1 )
CP
Mean heat capacity at constant pressure
(kJ·kg−1 ·K−1 , kJ·kmol−1 ·K−1 )
CV
Specific heat capacity at constant
volume (kJ·kg−1 ·K−1 ,
kJ·kmol−1 ·K−1 )
C∗
Solubility of solute in solvent (kg·kg
solvent−1 )
CC
Cycles of concentration for a cooling
tower (–)
COD
Chemical oxygen demand (kg·m−3 ,
mg·l−1 )
COP HP
Coefficient of performance of a heat
pump (–)
COP REF
Coefficient of performance of a
refrigeration system (–)
ASHELL
AF
Annualization factor for capital cost (–)
b
Capital cost law coefficient (units
depend on cost law), or
constant in cubic equation of state
(m3 ·kmol−1 ), or
correlating coefficient (units depend on
application), or
order of reaction (–)
bi
Bottoms flowrate of Component i
(kmol·s−1 , kmol·h−1 )
B
Bottoms flowrate in distillation
(kmol·s−1 , kmol·h−1 ), or
breadth of device (m), or
constant in vapor pressure correlation
(N·K·m−2 , bar·K), or
total moles in batch distillation (kmol)
BC
Baffle cut for shell-and-tube heat
exchangers (–)
xviii
Nomenclature
CP
Capacity parameter in distillation
(m·s−1 ) or
heat capacity flowrate (kW·K−1 ,
MW·K−1 )
CP EX
Heat capacity flowrate of heat engine
exhaust (kW·K−1 , MW·K−1 )
CW
Cooling water
d
Diameter (µm, m)
di
Distillate flowrate of Component i
(kmol·s−1 , kmol·h−1 )
dI
Inside diameter of pipe or tube (m)
D
Distillate flowrate (kmol·s−1 , kmol·h−1 )
DB
Tube bundle diameter for shell-and-tube
heat exchangers (m)
DS
Shell diameter for shell-and-tube heat
exchangers (m)
DCFRR
Discounted cash flowrate of return (%)
E
Activation energy of reaction
(kJ·kmol−1 ), or
entrainer flowrate in azeotropic and
extractive distillation (kg·s−1 ,
kmol·s−1 ), or
extract flowrate in liquid–liquid
extraction (kg·s−1 , kmol·s−1 ), or
stage efficiency in separation (–)
volumetric flowrate (m3 ·s−1 , m3 ·h−1 )
FLV
Liquid–vapor flow parameter in
distillation (–)
FT
Correction factor for noncountercurrent
flow in shell-and-tube heat
exchangers (–)
FTmin
Minimum acceptable FT for
noncountercurrent heat exchangers
(–)
g
Acceleration due to gravity (9.81
m·s−2 )
gij
Energy of interaction between
Molecules i and j in the NRTL
equation (kJ·kmol−1 )
G
Free energy (kJ), or
gas flowrate (kg·s−1 , kmol·s−1 )
Gi
Partial molar free energy of Component
i (kJ·kmol−1 )
O
Gi
Standard partial molar free energy of
Component i (kJ·kmol−1 )
h
Settling distance of particles (m)
hC
Condensing film heat transfer
coefficient (W·m−2 ·K−1 ,
kW·m−2 ·K−1 )
hI
Film heat transfer coefficient for the
inside (W·m−2 ·K−1 , kW·m−2 ·K−1 )
hIF
Fouling heat transfer coefficient for the
inside (W·m−2 ·K−1 , kW·m−2 ·K−1 )
EO
Overall stage efficiency in distillation
and absorption (–)
EP
Economic potential ($·y−1 )
f
Fuel-to-air ratio for gas turbine (–)
hL
Head loss in a pipe or pipe fitting (m)
fi
Capital cost installation factor for
Equipment i (–), or
feed flowrate of Component i
(kmol·s−1 , kmol·h−1 ), or
fugacity of Component i (N·m−2 , bar)
hNB
Nucleate boiling heat transfer
coefficient (W·m−2 ·K−1 ,
kW·m−2 ·K−1 )
hO
Film heat transfer coefficient for the
outside (W·m−2 ·K−1 , kW·m−2 ·K−1 )
fM
Capital cost factor to allow for material
of construction (–)
hOF
Fouling heat transfer coefficient for the
outside (W·m−2 ·K−1 , kW·m−2 ·K−1 )
fP
Capital cost factor to allow for design
pressure (–)
hW
Heat transfer coefficient for the tube
wall (W·m−2 ·K−1 , kW·m−2 ·K−1 )
fT
Capital cost factor to allow for design
temperature (–)
H
F
Feed flowrate (kg·s−1 , kg·h−1 ,
kmol·s−1 , kmol·h−1 ), or
future worth a sum of money allowing
for interest rates ($), or
Enthalpy (kJ, kJ·kg−1 , kJ·kmol−1 ), or
height (m), or
Henry’s Law Constant (N·m−2 , bar,
atm), or
stream enthalpy (kJ·s−1 , MJ·s−1 )
HT
Tray spacing (m)
Nomenclature xix
O
Hi
Standard heat of formation of
Component i (kJ·kmol−1 )
Ki
Ratio of vapor to liquid composition at
equilibrium for Component i (–)
H O
Standard heat of reaction (J, kJ)
KM,i
HCOMB
Heat of combustion (J·kmol−1 ,
kJ·kmol−1 )
Standard heat of combustion at 298 K
(J·kmol−1 , kJ·kmol−1 )
Heat to bring products from standard
temperature to the final temperature
(J·kmol−1 , kJ·kg−1 )
Heat to bring reactants from their initial
temperature to standard temperature
(J·kmol−1 , kJ·kmol−1 )
Enthalpy difference between generated
steam and boiler feedwater (kW,
MW)
Latent heat of vaporization (kJ·kg−1 ,
kJ·kmol−1 )
Equilibrium partition coefficient of
membrane for Component i (–)
Kp
Equilibrium constant of reaction based
on partial pressure in the vapor phase
(–)
KT
Parameter for terminal settling velocity
(m·s−1 )
Kx
Equilibrium constant of reaction based
on mole fraction in the liquid phase
(–)
Ky
Equilibrium constant of reaction based
on mole fraction in vapor phase (–)
L
Intercept ratio for turbines (–), or
length (m), or
liquid flowrate (kg·s−1 , kmol·s−1 ), or
number of independent loops in a
network (–)
LB
Distance between baffles in
shell-and-tube heat exchangers (m)
LP
Low pressure
m
Mass flowrate (kg·s−1 ), or
molar flowrate (kmol·s−1 ), or
number of items (–)
O
HCOMB
HP
HR
HSTEAM
HVAP
HETP
Height equivalent of a theoretical plate
(m)
HP
High pressure
−1
HR
Heat rate for gas turbine (kJ·kWh )
i
Fractional rate of interest on money
(–), or
number of ions (–)
I
Total number of hot streams (–)
J
Total number of cold streams (–)
M
k
Reaction rate constant (units depend on
order of reaction), or
thermal conductivity (W·m−1 ·K−1 ,
kW·m−1 ·K−1 )
Constant in capital cost correlations
(–), or
molar mass (kg·kmol−1 )
MP
Medium pressure
MC STEAM
Marginal cost of steam ($·t−1 )
kG,i
Mass transfer coefficient in the gas
phase (kmol·m−2 ·Pa−1 ·s−1 )
n
kij
Interaction parameter between
Components i and j in an equation
of state (–)
Number of items (–), or
number of years (–), or
polytropic coefficient (–), or
slope of Willans’ Line (kJ·kg−1 ,
MJ·kg−1 )
kL,i
Mass transfer coefficient in the liquid
phase (m·s−1 )
N
k0
Frequency factor for heat of reaction
(units depend on order of
reaction)
Number of compression stages (–), or
number of moles (kmol), or
number of theoretical stages (–), or
rate of transfer of a component
(kmol·s−1 ·m−3 )
K
Overall mass transfer coefficient
(kmol·Pa−1 ·m−2 ·s−1 ) or
total number of enthalpy intervals in
heat exchanger networks (–)
Ni
Number of moles of Component i
(kmol)
Ni0
Initial number of moles of Component
i (kmol)
NPT
Number of tube passes (–)
NR
Number of tube rows (–)
Ka
Equilibrium constant of reaction based
on activity (–)
xx
Nomenclature
NSHELLS
Number of number of 1–2 shells in
shell-and-tube heat exchangers (–)
NT
Number of tubes (–)
NUNITS
Number of units in a heat exchanger
network (–)
NC
qi
Individual stream heat duty for Stream
i (kJ·s−1 ), or
pure component property measuring the
molecular van der Waals surface area
for Molecule i in the UNIQUAC
Equation (–)
Number of components in a
multicomponent mixture (–)
Q
Heat duty (kW, MW)
Qc
Cooling duty (kW, MW)
NPV
Net present value ($)
Qc min
Target for cold utility (kW, MW)
p
Partial pressure (N·m−2 , bar)
QCOND
Condenser heat duty (kW, MW)
pC
Pitch configuration factor for tube
layout (–)
QEVAP
Evaporator heat duty (kW, MW)
QEX
pT
Tube pitch (m)
Heat duty for heat engine exhaust (kW,
MW)
P
Present worth of a future sum of money
($), or
pressure (N·m−2 , bar), or
probability (–), or
thermal effectiveness of 1–2
shell-and-tube heat exchanger (–)
QFEED
Heat duty to the feed (kW, MW)
QFUEL
Heat from fuel in a furnace, boiler, or
gas turbine (kW, MW)
QH
Heating duty (kW, MW)
QHmin
Target for hot utility (kW, MW)
PC
Critical pressure (N·m−2 , bar)
QHE
Heat engine heat duty (kW, MW)
Pmax
Maximum thermal effectiveness of 1–2
shell-and-tube heat exchangers (–)
QHEN
Heat exchanger network heat duty (kW,
MW)
PM,i
Permeability of Component i for a
membrane (kmol·m·s−1 ·m−2 ·bar−1 ,
kg solvent ·m−1 ·s−1 ·bar−1 )
QHP
Heat pump heat duty (kW, MW)
QLOSS
Stack loss from furnace, boiler, or gas
turbine (kW, MW)
QREACT
Reactor heating or cooling duty (kW,
MW)
P M,i
Permeance of Component i for a
membrane (m3 ·m−2 ·s−1 ·bar−1 )
PN−2N
Thermal effectiveness over NSHELLS
number of 1–2 shell-and-tube heat
exchangers in series (–)
QREB
Reboiler heat duty (kW, MW)
QREC
Heat recovery (kW, MW)
Thermal effectiveness over each 1–2
shell-and-tube heat exchanger in
series (–)
QSITE
Site heating demand (kW, MW)
QSTEAM
Heat input for steam generation (kW,
MW)
P SAT
Saturated liquid–vapor pressure
(N·m−2 , bar)
r
Pr
Prandtl number (–)
Molar ratio (–), or
pressure ratio (–), or
radius (m)
q
Heat flux (W·m−2 , kW·m−2 ), or
thermal condition of the feed in
distillation (–), or
Wegstein acceleration parameter for the
convergence of recycle calculations
(–)
ri
qC
Critical heat flux (W·m−2 , kW·m−2 )
Pure component property measuring the
molecular van der Waals volume for
Molecule i in the UNIQUAC
Equation (–), or
rate of reaction of Component i
(kmol−1 ·s−1 ), or
recovery of Component i in separation
(–)
qC1
Critical heat flux for a single tube
(W·m−2 , kW·m−2 )
R
Fractional recovery of a component in
separation (–), or
P1−2
Nomenclature xxi
heat capacity ratio of 1–2
shell-and-tube heat exchanger (–), or
raffinate flowrate in liquid–liquid
extraction (kg·s−1 , kmol·s−1 ), or
ratio of heat capacity flowrates (–), or
reflux ratio for distillation (–), or
removal ratio in effluent treatment (–),
or
residual error (units depend on
application), or
universal gas constant
(8314.5 N·m·kmol−1 K−1 =
J·kmol−1 K−1 ,
8.3145 kJ·kmol−1 ·K−1 )
TR
Reduced temperature T /TC (–)
TREB
Reboiler temperature (◦ C, K)
TS
Stream supply temperature (◦ C)
TSAT
Saturation temperature of boiling liquid
(◦ C, K)
TT
Stream target temperature (◦ C)
TTFT
Theoretical flame temperature (◦ C, K)
TW
Wall temperature (◦ C)
TWBT
Wet bulb temperature (◦ C)
T∗
Interval temperature (◦ C)
Rmin
Minimum reflux ratio (–)
TLM
RF
Ratio of actual to minimum reflux ratio
(–)
Logarithmic mean temperature
difference (◦ C, K)
Tmin
Minimum temperature difference
(◦ C, K)
TSAT
Difference in saturation temperature
(◦ C, K)
TTHRESHOLD
Threshold temperature difference (◦ C,
K)
TAC
Total annual cost ($·y−1 )
TOD
Total oxygen demand (kg·m−3 , mg·l−1 )
uij
Interaction parameter between Molecule
i and Molecule j in the UNIQUAC
Equation (kJ·kmol−1 )
Overall heat transfer coefficient
(W·m−2 ·K−1 , kW·m−2 ·K−1 )
RSITE
Site power-to-heat ratio (–)
ROI
Return on investment (%)
Re
Reynolds number (–)
s
Reactor space velocity (s−1 , min−1 ,
h−1 ), or
steam-to-air ratio for gas turbine (–)
S
Entropy (kJ·K−1 , kJ·kg−1 ·K−1 ,
kJ·kmol−1 ·K−1 ), or
number of streams in a heat exchanger
network (–), or
reactor selectivity (–), or
reboil ratio for distillation (–), or
selectivity of a reaction (–), or
slack variable in optimization (units
depend on application), or
solvent flowrate (kg·s−1 , kmol·s−1 ), or
stripping factor in absorption (–)
U
v
Velocity (m·s−1 )
vT
Terminal settling velocity (m·s−1 )
vV
Superficial vapor velocity in empty
column (m·s−1 )
V
Molar volume (m3 ·kmol−1 ), or
vapor flowrate (kg·s−1 , kmol·s−1 ), or
volume (m3 ), or
volume of gas or vapor adsorbed
(m3 ·kg−1 )
SC
Number of cold streams (–)
SH
Number of hot streams (–)
t
Time (s, h)
T
Temperature (◦ C, K)
TBPT
Normal boiling point (◦ C, K)
Vmin
TC
Critical temperature (K), or
temperature of heat sink (◦ C, K)
Minimum vapor flow (kg·s−1 ,
kmol·s−1 )
VF
Vapor fraction (–)
TCOND
Condenser temperature (◦ C, K)
w
TE
Equilibrium temperature (◦ C, K)
Mass of adsorbate per mass of
adsorbent (–)
Evaporation temperature (◦ C, K)
W
TEVAP
Shaft power (kW, MW), or
shaft work (kJ, MJ)
TFEED
Feed temperature (◦ C, K)
WGEN
Power generated (kW, MW)
WINT
Intercept of Willans’ Line (kW, MW)
TH
◦
Temperature of heat source ( C, K)
xxii
Nomenclature
WSITE
Site power demand (kW, MW)
x
Liquid-phase mole fraction (–) or
variable in optimization problem (–)
xF
Mole fraction in the feed (–)
xD
Mole fraction in the distillate (–)
X
Reactor conversion (–) or
wetness fraction of steam (–)
XE
Equilibrium reactor conversion (–)
XOPT
Optimal reactor conversion (–)
XP
Fraction of maximum thermal
effectiveness Pmax allowed in a 1–2
shell-and-tube heat exchanger (–)
XP
Cross-pinch heat transfer in heat
exchanger network (kW, MW)
y
Integer variable in optimization (–), or
vapor-phase mole fraction (–)
z
Elevation (m), or
feed mole fraction (–)
Z
Compressibility of a fluid (–)
ε
Extraction factor in liquid–liquid
extraction (–), or
pipe roughness (mm)
η
Carnot factor (–), or
efficiency (–)
ηBOILER
Boiler efficiency (–)
ηCOGEN
Cogeneration efficiency (–)
ηGT
Efficiency of gas turbine (–)
ηIS
Isentropic efficiency of compression or
expansion (–)
ηMECH
Mechanical efficiency of steam turbine
(–)
ηP
Polytropic efficiency of compression or
expansion (–)
ηPOWER
Power generation efficiency (–)
ηST
Efficiency of steam turbine (–)
θ
Fraction of feed permeated through
membrane (–), or
root of the Underwood Equation (–)
λ
Ratio of latent heats of vaporization (–)
λij
Energy parameter characterizing the
interaction of Molecule i with
Molecule j (kJ·kmol−1 )
Fluid viscosity (kg·m−1 ·s−1 ,
mN·s·m−2 = cP)
GREEK LETTERS
α
αij
Constant in cubic equation of state (–),
or
constants in vapor pressure correlation
(units depend on which constant), or
fraction open of a valve (–)
Ideal separation factor or selectivity of
membrane between Components i
and j (–), or
parameter characterizing the tendency
of Molecule i and Molecule j to be
distributed in a random fashion in the
NRTL equation (–), or
relative volatility between Components
i and j (–)
µ
π
Osmotic pressure (N·m−2 , bar)
ρ
Density (kg·m−3 , kmol·m−3 )
σ
Surface tension
(mN·m−1 = mJ·m−2 = dyne·cm−1 )
τ
Reactor space time (s, min, h) or
residence time (s, min, h)
φ
Cost-weighing factor applied to film
heat transfer coefficients to allow for
mixed materials of construction,
pressure rating, and equipment types
in heat exchanger networks (–), or
fugacity coefficient (–)
ω
Acentric factor (–)
αLH
Relative volatility between light and
heavy key components (–)
βij
Separation factor between Components
i and j (–)
γ
Ratio of heat capacities for gases and
vapors (–)
SUBSCRIPTS
γi
Activity coefficient for Component i
(–)
B
Blowdown, or
bottoms in distillation
δM
Membrane thickness (m)
BFW
Boiler feedwater
Nomenclature xxiii
cont
Contribution
M
Makeup
C
Cold stream, or
contaminant
MIX
Mixture
n
CN
Condensing
Stage number in distillation and
absorption
COND
Condensing conditions
out
Outlet
CP
Continuous phase
O
CW
Cooling water
Outside, or
standard conditions
D
Distillate in distillation
p
Stage number in distillation and
absorption
DS
De-superheating
prod
Products of reaction
e
Enhanced, or
end zone on the shell-side of a heat
exchanger, or
environment
P
Particle, or
permeate
react
Reactants
E
Extract in liquid–liquid extraction
R
Raffinate in liquid–liquid extraction
EVAP
Evaporator conditions
REACT
Reaction
EX
Exhaust
S
Solvent in liquid–liquid extraction
final
Final conditions in a batch
SAT
Saturated conditions
F
Feed, or
fluid
SF
Supplementary firing
SUP
Superheated conditions
T
Treatment
TW
Treated water
V
Vapor
w
Window section on the shell-side of a
heat exchanger
W
Conditions at the tube wall, or
water
∞
Conditions at distillate pinch point
G
Gas phase
H
Hot stream
HP
Heat pump, or
high pressure
i
Component number, or
stream number
I
Inside
IS
Isentropic
in
Inlet
j
Component number, or
stream number
SUPERSCRIPTS
k
Enthalpy interval number in heat
exchanger networks
I
Phase I
L
Liquid phase
II
Phase II
LP
Low pressure
III
Phase III
m
Stage number in distillation and
absorption
L
Liquid
O
Standard conditions
max
Maximum
V
Vapor
min
Minimum
*
Adjusted parameter
1
The Nature of Chemical Process Design and Integration
1.1 CHEMICAL PRODUCTS
Chemical products are essential to modern living standards.
Almost all aspects of everyday life are supported by
chemical products in one way or another. Yet, society tends
to take these products for granted, even though a high
quality of life fundamentally depends on them.
When considering the design of processes for the
manufacture of chemical products, the market into which
they are being sold fundamentally influences the objectives
and priorities in the design. Chemical products can be
divided into three broad classes:
1. Commodity or bulk chemicals: These are produced in
large volumes and purchased on the basis of chemical
composition, purity and price. Examples are sulfuric
acid, nitrogen, oxygen, ethylene and chlorine.
2. Fine chemicals: These are produced in small volumes
and purchased on the basis of chemical composition,
purity and price. Examples are chloropropylene oxide
(used for the manufacture of epoxy resins, ion-exchange
resins and other products), dimethyl formamide (used,
for example, as a solvent, reaction medium and intermediate in the manufacture of pharmaceuticals), n-butyric
acid (used in beverages, flavorings, fragrances and other
products) and barium titanate powder (used for the manufacture of electronic capacitors).
3. Specialty or effect or functional chemicals: These are
purchased because of their effect (or function), rather
than their chemical composition. Examples are pharmaceuticals, pesticides, dyestuffs, perfumes and flavorings.
Because commodity and fine chemicals tend to be purchased on the basis of their chemical composition alone,
they are undifferentiated. For example, there is nothing to
choose between 99.9% benzene made by one manufacturer
and that made by another manufacturer, other than price
and delivery issues. On the other hand, specialty chemicals
tend to be purchased on the basis of their effect or function
and are therefore differentiated. For example, competitive
pharmaceutical products are differentiated according to the
efficacy of the product, rather than chemical composition.
An adhesive is purchased on the basis of its ability to stick
things together, rather than its chemical composition and
so on.
Chemical Process Design and Integration R. Smith
2005 John Wiley & Sons, Ltd ISBNs: 0-471-48680-9 (HB); 0-471-48681-7 (PB)
However, undifferentiated and differentiated should be
thought of as relative terms rather than absolute terms for
chemical products. In practice, chemicals do not tend to
be completely undifferentiated or completely differentiated.
Commodity and fine chemical products might have impurity
specifications as well as purity specifications. Traces of
impurities can, in some cases, give some differentiation
between different manufacturers of commodity and fine
chemicals. For example, 99.9% acrylic acid might be
considered to be an undifferentiated product. However,
traces of impurities, at concentrations of a few parts per
million, can interfere with some of the reactions in which
it is used and can have important implications for some
of its uses. Such impurities might differ between different
manufacturing processes. Not all specialty products are
differentiated. For example, pharmaceutical products like
aspirin (acetylsalicylic acid) are undifferentiated. Different
manufacturers can produce aspirin and there is nothing to
choose between these products, other than the price and
differentiation created through marketing of the product.
Scale of production also differs between the three classes
of chemical products. Fine and specialty chemicals tend
to be produced in volumes less than 1000 t·y−1 . On the
other hand, commodity chemicals tend to be produced in
much larger volumes than this. However, the distinction
is again not so clear. Polymers are differentiated products
because they are purchased on the basis of their mechanical
properties, but can be produced in quantities significantly
higher than 1000 t·y−1 .
When a new chemical product is first developed, it
can often be protected by a patent in the early years of
commercial exploitation. For a product to be eligible to
be patented, it must be novel, useful and unobvious. If
patent protection can be obtained, this effectively gives
the producer a monopoly for commercial exploitation of
the product until the patent expires. Patent protection lasts
for 20 years from the filing date of the patent. Once the
patent expires, competitors can join in and manufacture the
product. If competitors cannot wait until the patent expires,
then alternative competing products must be developed.
Another way to protect a competitive edge for a new
product is to protect it by secrecy. The formula for CocaCola has been kept a secret for over 100 years. Potentially,
there is no time limit on such protection. However, for
the protection through secrecy to be viable, competitors
must not be able to reproduce the product from chemical
analysis. This is likely to be the case only for certain classes
of specialty and food products for which the properties of
2
The Nature of Chemical Process Design and Integration
the product depend on both the chemical composition and
the method of manufacture.
Figure 1.1 illustrates different product life cycles 1,2 . The
general trend is that when a new product is introduced
into the market, the sales grow slowly until the market
is established and then more rapidly once the market is
established. If there is patent protection, then competitors
will not be able to exploit the same product commercially
until the patent expires, when competitors can produce the
same product and take market share. It is expected that
competitive products will cause sales to diminish later in
the product life cycle until sales become so low that a
company would be expected to withdraw from the market.
In Figure 1.1, Product A appears to be a poor product that
has a short life with low sales volume. It might be that it
cannot compete well with other competitive products, and
alternative products quickly force the company out of that
business. However, a low sales volume is not the main
criterion to withdraw from the market. It might be that
a product with low volume finds a market niche and can
be sold for a high value. On the other hand, if it were
competing with other products with similar functions in
the same market sector, which keeps both the sale price
and volume low, then it would seem wise to withdraw
from the market. Product B in Figure 1.1 appears to be
a better product, showing a longer life cycle and higher
sales volume. This has patent protection but sales decrease
rapidly after patent protection is lost, leading to loss of
market through competition. Product C in Figure 1.1 is
a still better product. This shows high sales volume with
the life of the product extended through reformulation of
the product1 . Finally, Product D in Figure 1.1 shows a
product life cycle that is typical of commodity chemicals.
Commodity chemicals tend not to exhibit the same kind
of life cycles as fine and specialty chemicals. In the early
years of the commercial exploitation, the sales volume
grows rapidly to a high volume, but then does not decline
and enters a mature period of slow growth, or, in some
exceptional cases, slow decline. This is because commodity
chemicals tend to have a diverse range of uses. Even though
competition might take away some end uses, new end uses
are introduced, leading to an extended life cycle.
The different classes of chemical products will have
very different added value (the difference between the
selling price of the product and the purchase cost of
raw materials). Commodity chemicals tend to have low
added value, whereas fine and specialty chemicals tend to
have high added value. Commodity chemicals tend to be
produced in large volumes with low added value, while
fine and specialty chemicals tend to be produced in small
volumes with high added value.
Because of this, when designing a process for a
commodity chemical, it is usually important to keep
operating costs as low as possible. The capital cost of the
process will tend to be high relative to a process for fine or
specialty chemicals because of the scale of production.
When designing a process for specialty chemicals,
priority tends to be given to the product, rather than to
the process. This is because the unique function of th
Robin Smith
Centre for Process Integration,
School of Chemical Engineering and Analytical Science,
University of Manchester.
Chemical Process Design and Integration
Chemical Process Design and Integration
Robin Smith
Centre for Process Integration,
School of Chemical Engineering and Analytical Science,
University of Manchester.
Previous edition published by McGraw Hill
Copyright 2005
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Library of Congress Cataloging-in-Publication Data
Smith, R. (Robin)
Chemical process design and integration / Robin Smith.
p. cm.
Includes bibliographical references and index.
ISBN 0-471-48680-9 (HB) (acid-free paper) – ISBN 0-471-48681-7 (PB) (pbk. :
acid-free paper)
1. Chemical processes. I. Title.
TP155.7.S573 2005
660′ .2812 – dc22
2004014695
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN 0-471-48680-9 (cloth)
0-471-48681-7 (paper)
Typeset in 10/12pt Times by Laserwords Private Limited, Chennai, India
Printed and bound in Spain by Grafos, Barcelona
This book is printed on acid-free paper responsibly manufactured from sustainable forestry
in which at least two trees are planted for each one used for paper production.
To my family
Contents
Preface
xiii
Acknowledgements
Nomenclature
Chapter 1 The Nature of Chemical Process
Design and Integration
1.1 Chemical Products
1.2 Formulation of the Design Problem
1.3 Chemical Process Design and
Integration
1.4 The Hierarchy of Chemical Process
Design and Integration
1.5 Continuous and Batch Processes
1.6 New Design and Retrofit
1.7 Approaches to Chemical Process
Design and Integration
1.8 Process Control
1.9 The Nature of Chemical Process
Design and Integration – Summary
References
Chapter 2 Process Economics
2.1
2.2
2.3
2.4
2.5
2.6
2.7
The Role of Process Economics
Capital Cost for New Design
Capital Cost for Retrofit
Annualized Capital Cost
Operating Cost
Simple Economic Criteria
Project Cash Flow and Economic
Evaluation
2.8 Investment Criteria
2.9 Process Economics – Summary
2.10 Exercises
References
Chapter 3 Optimization
3.1
3.2
3.3
3.4
3.5
Objective Functions
Single-variable Optimization
Multivariable Optimization
Constrained Optimization
Linear Programming
xv
xvii
1
1
3
4
5
9
10
11
13
14
14
17
17
17
23
24
25
28
29
30
31
32
33
35
35
37
38
42
43
3.6
3.7
3.8
3.9
Nonlinear Programming
Profile Optimization
Structural Optimization
Solution of Equations
using Optimization
3.10 The Search for Global
Optimality
3.11 Summary – Optimization
3.12 Exercises
References
Chapter 4 Thermodynamic Properties and
Phase Equilibrium
4.1 Equations of State
4.2 Phase Equilibrium for Single
Components
4.3 Fugacity and Phase Equilibrium
4.4 Vapor–Liquid Equilibrium
4.5 Vapor–Liquid Equilibrium Based on
Activity Coefficient Models
4.6 Vapor–Liquid Equilibrium Based on
Equations of State
4.7 Calculation of Vapor–Liquid
Equilibrium
4.8 Liquid–Liquid Equilibrium
4.9 Liquid–Liquid Equilibrium Activity
Coefficient Models
4.10 Calculation of Liquid–Liquid
Equilibrium
4.11 Calculation of Enthalpy
4.12 Calculation of Entropy
4.13 Phase Equilibrium and Thermodynamic
Properties – Summary
4.14 Exercises
References
Chapter 5 Choice of Reactor I – Reactor
Performance
5.1
5.2
5.3
5.4
5.5
5.6
5.7
Reaction Path
Types of Reaction Systems
Reactor Performance
Rate of Reaction
Idealized Reactor Models
Choice of Idealized Reactor Model
Choice of Reactor Performance
45
46
48
52
53
54
54
56
57
57
59
60
60
62
64
64
70
71
71
72
74
74
74
76
77
77
78
81
82
83
90
94
viii
Contents
5.8 Choice of Reactor
Performance – Summary
5.9 Exercises
References
Chapter 6 Choice of Reactor II - Reactor
Conditions
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
Reaction Equilibrium
Reactor Temperature
Reactor Pressure
Reactor Phase
Reactor Concentration
Biochemical Reactions
Catalysts
Choice of Reactor
Conditions – Summary
6.9 Exercises
References
Chapter 7 Choice of Reactor III – Reactor
Configuration
7.1 Temperature Control
7.2 Catalyst Degradation
7.3 Gas–Liquid and Liquid–Liquid
Reactors
7.4 Reactor Configuration
7.5 Reactor Configuration for
Heterogeneous Solid-Catalyzed
Reactions
7.6 Reactor Configuration from
Optimization of a Superstructure
7.7 Choice of Reactor
Configuration – Summary
7.8 Exercises
References
Chapter 8 Choice of Separator for
Heterogeneous Mixtures
8.1 Homogeneous and Heterogeneous
Separation
8.2 Settling and Sedimentation
8.3 Inertial and Centrifugal Separation
8.4 Electrostatic Precipitation
8.5 Filtration
8.6 Scrubbing
8.7 Flotation
8.8 Drying
8.9 Separation of Heterogeneous
Mixtures – Summary
8.10 Exercises
References
94
95
96
97
97
100
107
108
109
114
114
117
118
120
121
121
123
124
127
133
133
139
139
140
143
143
143
147
149
150
151
152
153
154
154
155
Chapter 9 Choice of Separator for
Homogeneous Fluid Mixtures
I – Distillation
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
Single-Stage Separation
Distillation
Binary Distillation
Total and Minimum Reflux
Conditions for Multicomponent
Mixtures
Finite Reflux Conditions for
Multicomponent Mixtures
Choice of Operating Conditions
Limitations of Distillation
Separation of Homogeneous Fluid
Mixtures by Distillation – Summary
Exercises
References
Chapter 10 Choice of Separator for
Homogeneous Fluid Mixtures
II – Other Methods
10.1
10.2
10.3
10.4
10.5
10.6
10.7
Absorption and Stripping
Liquid–Liquid Extraction
Adsorption
Membranes
Crystallization
Evaporation
Separation of Homogeneous Fluid
Mixtures by Other
Methods – Summary
10.8 Exercises
References
Chapter 11 Distillation Sequencing
11.1 Distillation Sequencing Using
Simple Columns
11.2 Practical Constraints Restricting
Options
11.3 Choice of Sequence for Simple
Nonintegrated Distillation Columns
11.4 Distillation Sequencing Using
Columns With More Than Two
Products
11.5 Distillation Sequencing Using
Thermal Coupling
11.6 Retrofit of Distillation Sequences
11.7 Crude Oil Distillation
11.8 Distillation Sequencing Using
Optimization of a Superstructure
11.9 Distillation Sequencing – Summary
11.10 Exercises
References
157
157
157
160
163
170
175
176
177
178
179
181
181
184
189
193
203
206
208
209
209
211
211
211
212
217
220
224
225
228
230
231
232
Contents
Chapter 12 Distillation Sequencing for
Azeotropic Distillation
12.1 Azeotropic Systems
12.2 Change in Pressure
12.3 Representation of Azeotropic
Distillation
12.4 Distillation at Total Reflux
Conditions
12.5 Distillation at Minimum Reflux
Conditions
12.6 Distillation at Finite Reflux
Conditions
12.7 Distillation Sequencing Using an
Entrainer
12.8 Heterogeneous Azeotropic
Distillation
12.9 Entrainer Selection
12.10 Trade-offs in Azeotropic Distillation
12.11 Multicomponent Systems
12.12 Membrane Separation
12.13 Distillation Sequencing for
Azeotropic Distillation – Summary
12.14 Exercises
References
Chapter 13 Reaction, Separation and Recycle
Systems for Continuous Processes
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
13.10
13.11
The Function of Process Recycles
Recycles with Purges
Pumping and Compression
Simulation of Recycles
The Process Yield
Optimization of Reactor Conversion
Optimization of Processes Involving
a Purge
Hybrid Reaction and Separation
Feed, Product and Intermediate
Storage
Reaction, Separation and Recycle
Systems for Continuous
Processes – Summary
Exercises
References
Chapter 14 Reaction, Separation and Recycle
Systems for Batch Processes
14.1
14.2
14.3
14.4
14.5
Batch Processes
Batch Reactors
Batch Separation Processes
Gantt Charts
Production Schedules for Single
Products
235
235
235
236
238
242
243
14.6 Production Schedules for Multiple
Products
14.7 Equipment Cleaning and Material
Transfer
14.8 Synthesis of Reaction and
Separation Systems for Batch
Processes
14.9 Optimization of Batch Processes
14.10 Storage in Batch Processes
14.11 Reaction and Separation Systems for
Batch Processes – Summary
14.12 Exercises
References
ix
305
306
307
311
312
313
313
315
246
251
253
255
255
255
256
257
258
259
259
264
267
276
280
281
283
284
286
288
289
290
291
291
291
297
303
304
Chapter 15 Heat Exchanger Networks
I – Heat Transfer Equipment
15.1 Overall Heat Transfer Coefficients
15.2 Heat Transfer Coefficients and
Pressure Drops for Shell-and-Tube
Heat Exchangers
15.3 Temperature Differences in
Shell-and-Tube Heat Exchangers
15.4 Allocation of Fluids in
Shell-and-Tube Heat Exchangers
15.5 Extended Surface Tubes
15.6 Retrofit of Heat Exchangers
15.7 Condensers
15.8 Reboilers and Vaporizers
15.9 Other Types of Heat Exchange
Equipment
15.10 Fired Heaters
15.11 Heat Transfer
Equipment – Summary
15.12 Exercises
References
Chapter 16 Heat Exchanger Networks
II – Energy Targets
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
16.10
16.11
Composite Curves
The Heat Recovery Pinch
Threshold Problems
The Problem Table Algorithm
Nonglobal Minimum Temperature
Differences
Process Constraints
Utility Selection
Furnaces
Cogeneration (Combined Heat and
Power Generation)
Integration Of Heat Pumps
Heat Exchanger Network Energy
Targets – Summary
317
317
319
324
329
332
333
337
342
346
348
354
354
356
357
357
361
364
365
370
370
372
374
376
381
383
x
Contents
16.12 Exercises
References
Chapter 17 Heat Exchanger Networks
III – Capital and Total Cost
Targets
17.1
17.2
17.3
17.4
17.5
17.6
Number of Heat Exchange Units
Heat Exchange Area Targets
Number-of-shells Target
Capital Cost Targets
Total Cost Targets
Heat Exchanger Network and
Utilities Capital and Total
Costs – Summary
17.7 Exercises
References
Chapter 18 Heat Exchanger Networks
IV – Network Design
18.1
18.2
18.3
18.4
18.5
18.6
18.7
18.8
18.9
18.10
18.11
The Pinch Design Method
Design for Threshold Problems
Stream Splitting
Design for Multiple Pinches
Remaining Problem Analysis
Network Optimization
The Superstructure Approach to
Heat Exchanger Network Design
Retrofit of Heat Exchanger
Networks
Addition of New Heat Transfer Area
in Retrofit
Heat Exchanger Network
Design – Summary
Exercises
References
Chapter 19 Heat Exchanger Networks
V – Stream Data
19.1 Process Changes for Heat
Integration
19.2 The Trade-Offs Between Process
Changes, Utility Selection, Energy
Cost and Capital Cost
19.3 Data Extraction
19.4 Heat Exchanger Network Stream
Data – Summary
19.5 Exercises
References
383
385
387
387
388
392
393
395
395
396
397
399
399
404
405
408
411
413
416
419
424
425
425
428
429
429
429
430
437
437
438
Chapter 20 Heat Integration of Reactors
20.1 The Heat Integration Characteristics
of Reactors
20.2 Appropriate Placement of Reactors
20.3 Use of the Grand Composite Curve
for Heat Integration of Reactors
20.4 Evolving Reactor Design to Improve
Heat Integration
20.5 Heat Integration of
Reactors – Summary
Reference
Chapter 21 Heat Integration of Distillation
Columns
21.1 The Heat Integration Characteristics
of Distillation
21.2 The Appropriate Placement of
Distillation
21.3 Use of the Grand Composite Curve
for Heat Integration of Distillation
21.4 Evolving the Design of Simple
Distillation Columns to Improve
Heat Integration
21.5 Heat Pumping in Distillation
21.6 Capital Cost Considerations
21.7 Heat Integration Characteristics of
Distillation Sequences
21.8 Heat-integrated Distillation
Sequences Based on the
Optimization of a Superstructure
21.9 Heat Integration of Distillation
Columns – Summary
21.10 Exercises
References
Chapter 22 Heat Integration of Evaporators
and Dryers
22.1 The Heat Integration Characteristics
of Evaporators
22.2 Appropriate Placement of
Evaporators
22.3 Evolving Evaporator Design to
Improve Heat Integration
22.4 The Heat Integration Characteristics
of Dryers
22.5 Evolving Dryer Design to Improve
Heat Integration
22.6 Heat Integration of Evaporators and
Dryers – Summary
439
439
441
442
443
444
444
445
445
445
446
447
449
449
450
454
455
456
457
459
459
459
459
459
460
461
Contents
22.7 Exercises
References
Chapter 23 Steam Systems and Cogeneration
23.1
23.2
23.3
23.4
23.5
23.6
23.7
23.8
23.9
23.10
23.11
23.12
23.13
23.14
462
463
465
Boiler Feedwater Treatment
Steam Boilers
Steam Turbines
Gas Turbines
Steam System Configuration
Steam and Power Balances
Site Composite Curves
Cogeneration Targets
Optimization of Steam Levels
Site Power-to-heat Ratio
Optimizing Steam Systems
Steam Costs
Choice of Driver
Steam Systems and
Cogeneration – Summary
23.15 Exercises
References
466
468
471
477
482
484
487
490
493
496
498
502
506
Chapter 24 Cooling and Refrigeration Systems
513
24.1 Cooling Systems
24.2 Recirculating Cooling Water
Systems
24.3 Targeting Minimum Cooling Water
Flowrate
24.4 Design of Cooling Water Networks
24.5 Retrofit of Cooling Water Systems
24.6 Refrigeration Cycles
24.7 Process Expanders
24.8 Choice of Refrigerant for
Compression Refrigeration
24.9 Targeting Refrigeration Power for
Compression Refrigeration
24.10 Heat Integration of Compression
Refrigeration Processes
24.11 Mixed Refrigerants for Compression
Refrigeration
24.12 Absorption Refrigeration
24.13 Indirect Refrigeration
24.14 Cooling Water and Refrigeration
Systems – Summary
24.15 Exercises
References
Chapter 25 Environmental Design for
Atmospheric Emissions
25.1 Atmospheric Pollution
507
508
510
513
513
516
518
524
526
530
532
535
539
542
544
546
546
547
549
551
551
25.2 Sources of Atmospheric Pollution
25.3 Control of Solid Particulate
Emissions to Atmosphere
25.4 Control of VOC Emissions to
Atmosphere
25.5 Control of Sulfur Emissions
25.6 Control of Oxides of Nitrogen
Emissions
25.7 Control of Combustion Emissions
25.8 Atmospheric Dispersion
25.9 Environmental Design for
Atmospheric Emissions – Summary
25.10 Exercises
References
Chapter 26 Water System Design
26.1
26.2
26.3
26.4
26.5
26.6
26.7
26.8
26.9
26.10
26.11
26.12
26.13
26.14
26.15
26.16
Aqueous Contamination
Primary Treatment Processes
Biological Treatment Processes
Tertiary Treatment Processes
Water Use
Targeting Maximum Water Reuse
for Single Contaminants
Design for Maximum Water Reuse
for Single Contaminants
Targeting and Design for Maximum
Water Reuse Based on Optimization
of a Superstructure
Process Changes for Reduced Water
Consumption
Targeting Minimum Wastewater
Treatment Flowrate for Single
Contaminants
Design for Minimum Wastewater
Treatment Flowrate for Single
Contaminants
Regeneration of Wastewater
Targeting and Design for Effluent
Treatment and Regeneration Based
on Optimization of a Superstructure
Data Extraction
Water System Design – Summary
Exercises
References
Chapter 27 Inherent Safety
27.1
27.2
27.3
27.4
Fire
Explosion
Toxic Release
Intensification of Hazardous
Materials
xi
552
553
554
565
569
573
574
575
576
579
581
583
585
588
591
593
594
596
604
606
607
610
613
616
617
620
620
623
625
625
626
627
628
xii
Contents
27.5 Attenuation of Hazardous Materials
27.6 Quantitative Measures of Inherent
Safety
27.7 Inherent Safety – Summary
27.8 Exercises
References
Chapter 28 Clean Process Technology
28.1 Sources of Waste from Chemical
Production
28.2 Clean Process Technology for
Chemical Reactors
28.3 Clean Process Technology for
Separation and Recycle Systems
28.4 Clean Process Technology for
Process Operations
28.5 Clean Process Technology for
Utility Systems
28.6 Trading off Clean Process
Technology Options
28.7 Life Cycle Analysis
28.8 Clean Process Technology –
Summary
28.9 Exercises
References
Chapter 29 Overall Strategy for Chemical
Process Design and Integration
29.1 Objectives
29.2 The Hierarchy
29.3 The Final Design
B.2 Centrifugal Compressors
B.3 Staged Compression
658
659
Appendix C Heat Transfer Coefficients and
Pressure Drop in Shell-and-tube
Heat Exchangers
661
630
631
632
632
633
C.1 Pressure Drop and Heat Transfer
Correlations for the Tube-Side
C.2 Pressure Drop and Heat Transfer
Correlations for the Shell-Side
References
635
635
662
666
636
637
Appendix D The Maximum Thermal
Effectiveness for 1–2
Shell-and-tube Heat Exchangers
667
Appendix E Expression for the Minimum
Number of 1–2 Shell-and-tube
Heat Exchangers for a Given Unit
669
Appendix F Algorithm for the Heat Exchanger
Network Area Target
671
Appendix G Algorithm for the Heat Exchanger
Network Number of Shells Target
673
G.1 Minimum Area Target for Networks
of 1–2 Shells
References
674
677
642
643
644
645
646
646
647
649
649
649
651
Appendix A Annualization of Capital Cost
653
Appendix B Gas Compression
655
Appendix H Algorithm for Heat Exchanger
Network Capital Cost Targets
Index
B.1 Reciprocating Compressors
661
655
677
679
Preface
This book deals with the design and integration of chemical
processes, emphasizing the conceptual issues that are
fundamental to the creation of the process. Chemical
process design requires the selection of a series of
processing steps and their integration to form a complete
manufacturing system. The text emphasizes both the design
and selection of the steps as individual operations and their
integration to form an efficient process. Also, the process
will normally operate as part of an integrated manufacturing
site consisting of a number of processes serviced by a
common utility system. The design of utility systems has
been dealt with so that the interactions between processes
and the utility system and the interactions between different
processes through the utility system can be exploited to
maximize the performance of the site as a whole. Thus,
the text integrates equipment, process and utility system
design.
Chemical processing should form part of a sustainable
industrial activity. For chemical processing, this means
that processes should use raw materials as efficiently as is
economic and practicable, both to prevent the production
of waste that can be environmentally harmful and to
preserve the reserves of raw materials as much as possible.
Processes should use as little energy as is economic and
practicable, both to prevent the buildup of carbon dioxide
in the atmosphere from burning fossil fuels and to preserve
reserves of fossil fuels. Water must also be consumed in
sustainable quantities that do not cause deterioration in the
quality of the water source and the long-term quantity of the
reserves. Aqueous and atmospheric emissions must not be
environmentally harmful, and solid waste to landfill must
be avoided. Finally, all aspects of chemical processing must
feature good health and safety practice.
It is important for the designer to understand the
limitations of the methods used in chemical process design.
The best way to understand the limitations is to understand
the derivations of the equations used and the assumptions
on which the equations are based. Where practical, the
derivation of the design equations has been included in
the text.
The book is intended to provide a practical guide to
chemical process design and integration for undergraduate
and postgraduate students of chemical engineering, practicing process designers and chemical engineers and applied
chemists working in process development. For undergraduate studies, the text assumes basic knowledge of material and energy balances, fluid mechanics, heat and mass
transfer phenomena and thermodynamics, together with
basic spreadsheeting skills. Examples have been included
throughout the text. Most of these examples do not require
specialist software and can be solved using spreadsheet software. Finally, a number of exercises have been added at
the end of each chapter to allow the reader to practice the
calculation procedures.
Robin Smith
Acknowledgements
The author would like to express gratitude to a number
of people who have helped in the preparation and have
reviewed parts of the text.
From The University of Manchester: Prof Peter Heggs,
Prof Ferda Mavituna, Megan Jobson, Nan Zhang, Constantinos Theodoropoulos, Jin-Kuk Kim, Kah Loong Choong,
Dhaval Dave, Frank Del Nogal, Ramona Dragomir, Sungwon
Hwang, Santosh Jain, Boondarik Leewongtanawit, Guilian Liu, Vikas Rastogi, Clemente Rodriguez, Ramagopal
Uppaluri, Priti Vanage, Pertar Verbanov, Jiaona Wang, Wenling Zhang.
From Alias, UK: David Lott.
From AspenTech: Ian Moore, Eric Petela, Ian Sinclair,
Oliver Wahnschafft.
From CANMET, Canada: Alberto Alva-Argaez, Abdelaziz Hammache, Luciana Savulescu, Mikhail Sorin.
From DuPont Taiwan: Janice Kuo.
From Monash University, Australia: David Brennan,
Andrew Hoadley.
From UOP, Des Plaines, USA: David Hamm, Greg
Maher.
Gratitude is also expressed to Simon Perry, Gareth
Maguire, Victoria Woods and Mathew Smith for help in
the preparation of the figures.
Finally, gratitude is expressed to all of the member
companies of the Process Integration Research Consortium,
both past and present. Their support has made a considerable
contribution to research in the area, and hence to this text.
Nomenclature
a
A
Activity (–), or
constant in cubic equation of state
(N·m4 ·kmol−2 ), or
correlating coefficient (units depend on
application), or
cost law coefficient ($), or
order of reaction (–)
Absorption factor in absorption (–), or
annual cash flow ($), or
constant in vapor pressure correlation
(N·m−2 , bar), or
heat exchanger area (m2 )
ACF
Annual cash flow ($·y−1 )
ADCF
Annual discounted cash flow ($·y−1 )
AI
Heat transfer area on the inside of tubes
(m2 ), or
interfacial area (m2 , m2 ·m−3 )
BOD
Biological oxygen demand (kg·m−3 ,
mg·l−1 )
c
Capital cost law coefficient (–), or
order of reaction (–)
cD
Drag coefficient (–)
cF
Fanning friction factor (–)
cL
Loss coefficient for pipe or pipe fitting
(–)
C
Concentration (kg·m−3 , kmol·m−3 ,
ppm), or
constant in vapor pressure correlation
(K), or
number of components (separate
systems) in network design (–)
CB
Base capital cost of equipment ($)
Ce
Environmental discharge concentration
(ppm)
AM
Membrane area (m2 )
ANETWORK
Heat exchanger network area (m2 )
CE
AO
Heat transfer area on the outside of
tubes (m2 )
Equipment capital cost ($), or
unit cost of energy ($·kW−1 , $·MW−1 )
CF
Heat exchanger area for an individual
shell (m2 )
Fixed capital cost of complete
installation ($)
CP
Specific heat capacity at constant
pressure (kJ·kg−1 ·K−1 ,
kJ·kmol−1 ·K−1 )
CP
Mean heat capacity at constant pressure
(kJ·kg−1 ·K−1 , kJ·kmol−1 ·K−1 )
CV
Specific heat capacity at constant
volume (kJ·kg−1 ·K−1 ,
kJ·kmol−1 ·K−1 )
C∗
Solubility of solute in solvent (kg·kg
solvent−1 )
CC
Cycles of concentration for a cooling
tower (–)
COD
Chemical oxygen demand (kg·m−3 ,
mg·l−1 )
COP HP
Coefficient of performance of a heat
pump (–)
COP REF
Coefficient of performance of a
refrigeration system (–)
ASHELL
AF
Annualization factor for capital cost (–)
b
Capital cost law coefficient (units
depend on cost law), or
constant in cubic equation of state
(m3 ·kmol−1 ), or
correlating coefficient (units depend on
application), or
order of reaction (–)
bi
Bottoms flowrate of Component i
(kmol·s−1 , kmol·h−1 )
B
Bottoms flowrate in distillation
(kmol·s−1 , kmol·h−1 ), or
breadth of device (m), or
constant in vapor pressure correlation
(N·K·m−2 , bar·K), or
total moles in batch distillation (kmol)
BC
Baffle cut for shell-and-tube heat
exchangers (–)
xviii
Nomenclature
CP
Capacity parameter in distillation
(m·s−1 ) or
heat capacity flowrate (kW·K−1 ,
MW·K−1 )
CP EX
Heat capacity flowrate of heat engine
exhaust (kW·K−1 , MW·K−1 )
CW
Cooling water
d
Diameter (µm, m)
di
Distillate flowrate of Component i
(kmol·s−1 , kmol·h−1 )
dI
Inside diameter of pipe or tube (m)
D
Distillate flowrate (kmol·s−1 , kmol·h−1 )
DB
Tube bundle diameter for shell-and-tube
heat exchangers (m)
DS
Shell diameter for shell-and-tube heat
exchangers (m)
DCFRR
Discounted cash flowrate of return (%)
E
Activation energy of reaction
(kJ·kmol−1 ), or
entrainer flowrate in azeotropic and
extractive distillation (kg·s−1 ,
kmol·s−1 ), or
extract flowrate in liquid–liquid
extraction (kg·s−1 , kmol·s−1 ), or
stage efficiency in separation (–)
volumetric flowrate (m3 ·s−1 , m3 ·h−1 )
FLV
Liquid–vapor flow parameter in
distillation (–)
FT
Correction factor for noncountercurrent
flow in shell-and-tube heat
exchangers (–)
FTmin
Minimum acceptable FT for
noncountercurrent heat exchangers
(–)
g
Acceleration due to gravity (9.81
m·s−2 )
gij
Energy of interaction between
Molecules i and j in the NRTL
equation (kJ·kmol−1 )
G
Free energy (kJ), or
gas flowrate (kg·s−1 , kmol·s−1 )
Gi
Partial molar free energy of Component
i (kJ·kmol−1 )
O
Gi
Standard partial molar free energy of
Component i (kJ·kmol−1 )
h
Settling distance of particles (m)
hC
Condensing film heat transfer
coefficient (W·m−2 ·K−1 ,
kW·m−2 ·K−1 )
hI
Film heat transfer coefficient for the
inside (W·m−2 ·K−1 , kW·m−2 ·K−1 )
hIF
Fouling heat transfer coefficient for the
inside (W·m−2 ·K−1 , kW·m−2 ·K−1 )
EO
Overall stage efficiency in distillation
and absorption (–)
EP
Economic potential ($·y−1 )
f
Fuel-to-air ratio for gas turbine (–)
hL
Head loss in a pipe or pipe fitting (m)
fi
Capital cost installation factor for
Equipment i (–), or
feed flowrate of Component i
(kmol·s−1 , kmol·h−1 ), or
fugacity of Component i (N·m−2 , bar)
hNB
Nucleate boiling heat transfer
coefficient (W·m−2 ·K−1 ,
kW·m−2 ·K−1 )
hO
Film heat transfer coefficient for the
outside (W·m−2 ·K−1 , kW·m−2 ·K−1 )
fM
Capital cost factor to allow for material
of construction (–)
hOF
Fouling heat transfer coefficient for the
outside (W·m−2 ·K−1 , kW·m−2 ·K−1 )
fP
Capital cost factor to allow for design
pressure (–)
hW
Heat transfer coefficient for the tube
wall (W·m−2 ·K−1 , kW·m−2 ·K−1 )
fT
Capital cost factor to allow for design
temperature (–)
H
F
Feed flowrate (kg·s−1 , kg·h−1 ,
kmol·s−1 , kmol·h−1 ), or
future worth a sum of money allowing
for interest rates ($), or
Enthalpy (kJ, kJ·kg−1 , kJ·kmol−1 ), or
height (m), or
Henry’s Law Constant (N·m−2 , bar,
atm), or
stream enthalpy (kJ·s−1 , MJ·s−1 )
HT
Tray spacing (m)
Nomenclature xix
O
Hi
Standard heat of formation of
Component i (kJ·kmol−1 )
Ki
Ratio of vapor to liquid composition at
equilibrium for Component i (–)
H O
Standard heat of reaction (J, kJ)
KM,i
HCOMB
Heat of combustion (J·kmol−1 ,
kJ·kmol−1 )
Standard heat of combustion at 298 K
(J·kmol−1 , kJ·kmol−1 )
Heat to bring products from standard
temperature to the final temperature
(J·kmol−1 , kJ·kg−1 )
Heat to bring reactants from their initial
temperature to standard temperature
(J·kmol−1 , kJ·kmol−1 )
Enthalpy difference between generated
steam and boiler feedwater (kW,
MW)
Latent heat of vaporization (kJ·kg−1 ,
kJ·kmol−1 )
Equilibrium partition coefficient of
membrane for Component i (–)
Kp
Equilibrium constant of reaction based
on partial pressure in the vapor phase
(–)
KT
Parameter for terminal settling velocity
(m·s−1 )
Kx
Equilibrium constant of reaction based
on mole fraction in the liquid phase
(–)
Ky
Equilibrium constant of reaction based
on mole fraction in vapor phase (–)
L
Intercept ratio for turbines (–), or
length (m), or
liquid flowrate (kg·s−1 , kmol·s−1 ), or
number of independent loops in a
network (–)
LB
Distance between baffles in
shell-and-tube heat exchangers (m)
LP
Low pressure
m
Mass flowrate (kg·s−1 ), or
molar flowrate (kmol·s−1 ), or
number of items (–)
O
HCOMB
HP
HR
HSTEAM
HVAP
HETP
Height equivalent of a theoretical plate
(m)
HP
High pressure
−1
HR
Heat rate for gas turbine (kJ·kWh )
i
Fractional rate of interest on money
(–), or
number of ions (–)
I
Total number of hot streams (–)
J
Total number of cold streams (–)
M
k
Reaction rate constant (units depend on
order of reaction), or
thermal conductivity (W·m−1 ·K−1 ,
kW·m−1 ·K−1 )
Constant in capital cost correlations
(–), or
molar mass (kg·kmol−1 )
MP
Medium pressure
MC STEAM
Marginal cost of steam ($·t−1 )
kG,i
Mass transfer coefficient in the gas
phase (kmol·m−2 ·Pa−1 ·s−1 )
n
kij
Interaction parameter between
Components i and j in an equation
of state (–)
Number of items (–), or
number of years (–), or
polytropic coefficient (–), or
slope of Willans’ Line (kJ·kg−1 ,
MJ·kg−1 )
kL,i
Mass transfer coefficient in the liquid
phase (m·s−1 )
N
k0
Frequency factor for heat of reaction
(units depend on order of
reaction)
Number of compression stages (–), or
number of moles (kmol), or
number of theoretical stages (–), or
rate of transfer of a component
(kmol·s−1 ·m−3 )
K
Overall mass transfer coefficient
(kmol·Pa−1 ·m−2 ·s−1 ) or
total number of enthalpy intervals in
heat exchanger networks (–)
Ni
Number of moles of Component i
(kmol)
Ni0
Initial number of moles of Component
i (kmol)
NPT
Number of tube passes (–)
NR
Number of tube rows (–)
Ka
Equilibrium constant of reaction based
on activity (–)
xx
Nomenclature
NSHELLS
Number of number of 1–2 shells in
shell-and-tube heat exchangers (–)
NT
Number of tubes (–)
NUNITS
Number of units in a heat exchanger
network (–)
NC
qi
Individual stream heat duty for Stream
i (kJ·s−1 ), or
pure component property measuring the
molecular van der Waals surface area
for Molecule i in the UNIQUAC
Equation (–)
Number of components in a
multicomponent mixture (–)
Q
Heat duty (kW, MW)
Qc
Cooling duty (kW, MW)
NPV
Net present value ($)
Qc min
Target for cold utility (kW, MW)
p
Partial pressure (N·m−2 , bar)
QCOND
Condenser heat duty (kW, MW)
pC
Pitch configuration factor for tube
layout (–)
QEVAP
Evaporator heat duty (kW, MW)
QEX
pT
Tube pitch (m)
Heat duty for heat engine exhaust (kW,
MW)
P
Present worth of a future sum of money
($), or
pressure (N·m−2 , bar), or
probability (–), or
thermal effectiveness of 1–2
shell-and-tube heat exchanger (–)
QFEED
Heat duty to the feed (kW, MW)
QFUEL
Heat from fuel in a furnace, boiler, or
gas turbine (kW, MW)
QH
Heating duty (kW, MW)
QHmin
Target for hot utility (kW, MW)
PC
Critical pressure (N·m−2 , bar)
QHE
Heat engine heat duty (kW, MW)
Pmax
Maximum thermal effectiveness of 1–2
shell-and-tube heat exchangers (–)
QHEN
Heat exchanger network heat duty (kW,
MW)
PM,i
Permeability of Component i for a
membrane (kmol·m·s−1 ·m−2 ·bar−1 ,
kg solvent ·m−1 ·s−1 ·bar−1 )
QHP
Heat pump heat duty (kW, MW)
QLOSS
Stack loss from furnace, boiler, or gas
turbine (kW, MW)
QREACT
Reactor heating or cooling duty (kW,
MW)
P M,i
Permeance of Component i for a
membrane (m3 ·m−2 ·s−1 ·bar−1 )
PN−2N
Thermal effectiveness over NSHELLS
number of 1–2 shell-and-tube heat
exchangers in series (–)
QREB
Reboiler heat duty (kW, MW)
QREC
Heat recovery (kW, MW)
Thermal effectiveness over each 1–2
shell-and-tube heat exchanger in
series (–)
QSITE
Site heating demand (kW, MW)
QSTEAM
Heat input for steam generation (kW,
MW)
P SAT
Saturated liquid–vapor pressure
(N·m−2 , bar)
r
Pr
Prandtl number (–)
Molar ratio (–), or
pressure ratio (–), or
radius (m)
q
Heat flux (W·m−2 , kW·m−2 ), or
thermal condition of the feed in
distillation (–), or
Wegstein acceleration parameter for the
convergence of recycle calculations
(–)
ri
qC
Critical heat flux (W·m−2 , kW·m−2 )
Pure component property measuring the
molecular van der Waals volume for
Molecule i in the UNIQUAC
Equation (–), or
rate of reaction of Component i
(kmol−1 ·s−1 ), or
recovery of Component i in separation
(–)
qC1
Critical heat flux for a single tube
(W·m−2 , kW·m−2 )
R
Fractional recovery of a component in
separation (–), or
P1−2
Nomenclature xxi
heat capacity ratio of 1–2
shell-and-tube heat exchanger (–), or
raffinate flowrate in liquid–liquid
extraction (kg·s−1 , kmol·s−1 ), or
ratio of heat capacity flowrates (–), or
reflux ratio for distillation (–), or
removal ratio in effluent treatment (–),
or
residual error (units depend on
application), or
universal gas constant
(8314.5 N·m·kmol−1 K−1 =
J·kmol−1 K−1 ,
8.3145 kJ·kmol−1 ·K−1 )
TR
Reduced temperature T /TC (–)
TREB
Reboiler temperature (◦ C, K)
TS
Stream supply temperature (◦ C)
TSAT
Saturation temperature of boiling liquid
(◦ C, K)
TT
Stream target temperature (◦ C)
TTFT
Theoretical flame temperature (◦ C, K)
TW
Wall temperature (◦ C)
TWBT
Wet bulb temperature (◦ C)
T∗
Interval temperature (◦ C)
Rmin
Minimum reflux ratio (–)
TLM
RF
Ratio of actual to minimum reflux ratio
(–)
Logarithmic mean temperature
difference (◦ C, K)
Tmin
Minimum temperature difference
(◦ C, K)
TSAT
Difference in saturation temperature
(◦ C, K)
TTHRESHOLD
Threshold temperature difference (◦ C,
K)
TAC
Total annual cost ($·y−1 )
TOD
Total oxygen demand (kg·m−3 , mg·l−1 )
uij
Interaction parameter between Molecule
i and Molecule j in the UNIQUAC
Equation (kJ·kmol−1 )
Overall heat transfer coefficient
(W·m−2 ·K−1 , kW·m−2 ·K−1 )
RSITE
Site power-to-heat ratio (–)
ROI
Return on investment (%)
Re
Reynolds number (–)
s
Reactor space velocity (s−1 , min−1 ,
h−1 ), or
steam-to-air ratio for gas turbine (–)
S
Entropy (kJ·K−1 , kJ·kg−1 ·K−1 ,
kJ·kmol−1 ·K−1 ), or
number of streams in a heat exchanger
network (–), or
reactor selectivity (–), or
reboil ratio for distillation (–), or
selectivity of a reaction (–), or
slack variable in optimization (units
depend on application), or
solvent flowrate (kg·s−1 , kmol·s−1 ), or
stripping factor in absorption (–)
U
v
Velocity (m·s−1 )
vT
Terminal settling velocity (m·s−1 )
vV
Superficial vapor velocity in empty
column (m·s−1 )
V
Molar volume (m3 ·kmol−1 ), or
vapor flowrate (kg·s−1 , kmol·s−1 ), or
volume (m3 ), or
volume of gas or vapor adsorbed
(m3 ·kg−1 )
SC
Number of cold streams (–)
SH
Number of hot streams (–)
t
Time (s, h)
T
Temperature (◦ C, K)
TBPT
Normal boiling point (◦ C, K)
Vmin
TC
Critical temperature (K), or
temperature of heat sink (◦ C, K)
Minimum vapor flow (kg·s−1 ,
kmol·s−1 )
VF
Vapor fraction (–)
TCOND
Condenser temperature (◦ C, K)
w
TE
Equilibrium temperature (◦ C, K)
Mass of adsorbate per mass of
adsorbent (–)
Evaporation temperature (◦ C, K)
W
TEVAP
Shaft power (kW, MW), or
shaft work (kJ, MJ)
TFEED
Feed temperature (◦ C, K)
WGEN
Power generated (kW, MW)
WINT
Intercept of Willans’ Line (kW, MW)
TH
◦
Temperature of heat source ( C, K)
xxii
Nomenclature
WSITE
Site power demand (kW, MW)
x
Liquid-phase mole fraction (–) or
variable in optimization problem (–)
xF
Mole fraction in the feed (–)
xD
Mole fraction in the distillate (–)
X
Reactor conversion (–) or
wetness fraction of steam (–)
XE
Equilibrium reactor conversion (–)
XOPT
Optimal reactor conversion (–)
XP
Fraction of maximum thermal
effectiveness Pmax allowed in a 1–2
shell-and-tube heat exchanger (–)
XP
Cross-pinch heat transfer in heat
exchanger network (kW, MW)
y
Integer variable in optimization (–), or
vapor-phase mole fraction (–)
z
Elevation (m), or
feed mole fraction (–)
Z
Compressibility of a fluid (–)
ε
Extraction factor in liquid–liquid
extraction (–), or
pipe roughness (mm)
η
Carnot factor (–), or
efficiency (–)
ηBOILER
Boiler efficiency (–)
ηCOGEN
Cogeneration efficiency (–)
ηGT
Efficiency of gas turbine (–)
ηIS
Isentropic efficiency of compression or
expansion (–)
ηMECH
Mechanical efficiency of steam turbine
(–)
ηP
Polytropic efficiency of compression or
expansion (–)
ηPOWER
Power generation efficiency (–)
ηST
Efficiency of steam turbine (–)
θ
Fraction of feed permeated through
membrane (–), or
root of the Underwood Equation (–)
λ
Ratio of latent heats of vaporization (–)
λij
Energy parameter characterizing the
interaction of Molecule i with
Molecule j (kJ·kmol−1 )
Fluid viscosity (kg·m−1 ·s−1 ,
mN·s·m−2 = cP)
GREEK LETTERS
α
αij
Constant in cubic equation of state (–),
or
constants in vapor pressure correlation
(units depend on which constant), or
fraction open of a valve (–)
Ideal separation factor or selectivity of
membrane between Components i
and j (–), or
parameter characterizing the tendency
of Molecule i and Molecule j to be
distributed in a random fashion in the
NRTL equation (–), or
relative volatility between Components
i and j (–)
µ
π
Osmotic pressure (N·m−2 , bar)
ρ
Density (kg·m−3 , kmol·m−3 )
σ
Surface tension
(mN·m−1 = mJ·m−2 = dyne·cm−1 )
τ
Reactor space time (s, min, h) or
residence time (s, min, h)
φ
Cost-weighing factor applied to film
heat transfer coefficients to allow for
mixed materials of construction,
pressure rating, and equipment types
in heat exchanger networks (–), or
fugacity coefficient (–)
ω
Acentric factor (–)
αLH
Relative volatility between light and
heavy key components (–)
βij
Separation factor between Components
i and j (–)
γ
Ratio of heat capacities for gases and
vapors (–)
SUBSCRIPTS
γi
Activity coefficient for Component i
(–)
B
Blowdown, or
bottoms in distillation
δM
Membrane thickness (m)
BFW
Boiler feedwater
Nomenclature xxiii
cont
Contribution
M
Makeup
C
Cold stream, or
contaminant
MIX
Mixture
n
CN
Condensing
Stage number in distillation and
absorption
COND
Condensing conditions
out
Outlet
CP
Continuous phase
O
CW
Cooling water
Outside, or
standard conditions
D
Distillate in distillation
p
Stage number in distillation and
absorption
DS
De-superheating
prod
Products of reaction
e
Enhanced, or
end zone on the shell-side of a heat
exchanger, or
environment
P
Particle, or
permeate
react
Reactants
E
Extract in liquid–liquid extraction
R
Raffinate in liquid–liquid extraction
EVAP
Evaporator conditions
REACT
Reaction
EX
Exhaust
S
Solvent in liquid–liquid extraction
final
Final conditions in a batch
SAT
Saturated conditions
F
Feed, or
fluid
SF
Supplementary firing
SUP
Superheated conditions
T
Treatment
TW
Treated water
V
Vapor
w
Window section on the shell-side of a
heat exchanger
W
Conditions at the tube wall, or
water
∞
Conditions at distillate pinch point
G
Gas phase
H
Hot stream
HP
Heat pump, or
high pressure
i
Component number, or
stream number
I
Inside
IS
Isentropic
in
Inlet
j
Component number, or
stream number
SUPERSCRIPTS
k
Enthalpy interval number in heat
exchanger networks
I
Phase I
L
Liquid phase
II
Phase II
LP
Low pressure
III
Phase III
m
Stage number in distillation and
absorption
L
Liquid
O
Standard conditions
max
Maximum
V
Vapor
min
Minimum
*
Adjusted parameter
1
The Nature of Chemical Process Design and Integration
1.1 CHEMICAL PRODUCTS
Chemical products are essential to modern living standards.
Almost all aspects of everyday life are supported by
chemical products in one way or another. Yet, society tends
to take these products for granted, even though a high
quality of life fundamentally depends on them.
When considering the design of processes for the
manufacture of chemical products, the market into which
they are being sold fundamentally influences the objectives
and priorities in the design. Chemical products can be
divided into three broad classes:
1. Commodity or bulk chemicals: These are produced in
large volumes and purchased on the basis of chemical
composition, purity and price. Examples are sulfuric
acid, nitrogen, oxygen, ethylene and chlorine.
2. Fine chemicals: These are produced in small volumes
and purchased on the basis of chemical composition,
purity and price. Examples are chloropropylene oxide
(used for the manufacture of epoxy resins, ion-exchange
resins and other products), dimethyl formamide (used,
for example, as a solvent, reaction medium and intermediate in the manufacture of pharmaceuticals), n-butyric
acid (used in beverages, flavorings, fragrances and other
products) and barium titanate powder (used for the manufacture of electronic capacitors).
3. Specialty or effect or functional chemicals: These are
purchased because of their effect (or function), rather
than their chemical composition. Examples are pharmaceuticals, pesticides, dyestuffs, perfumes and flavorings.
Because commodity and fine chemicals tend to be purchased on the basis of their chemical composition alone,
they are undifferentiated. For example, there is nothing to
choose between 99.9% benzene made by one manufacturer
and that made by another manufacturer, other than price
and delivery issues. On the other hand, specialty chemicals
tend to be purchased on the basis of their effect or function
and are therefore differentiated. For example, competitive
pharmaceutical products are differentiated according to the
efficacy of the product, rather than chemical composition.
An adhesive is purchased on the basis of its ability to stick
things together, rather than its chemical composition and
so on.
Chemical Process Design and Integration R. Smith
2005 John Wiley & Sons, Ltd ISBNs: 0-471-48680-9 (HB); 0-471-48681-7 (PB)
However, undifferentiated and differentiated should be
thought of as relative terms rather than absolute terms for
chemical products. In practice, chemicals do not tend to
be completely undifferentiated or completely differentiated.
Commodity and fine chemical products might have impurity
specifications as well as purity specifications. Traces of
impurities can, in some cases, give some differentiation
between different manufacturers of commodity and fine
chemicals. For example, 99.9% acrylic acid might be
considered to be an undifferentiated product. However,
traces of impurities, at concentrations of a few parts per
million, can interfere with some of the reactions in which
it is used and can have important implications for some
of its uses. Such impurities might differ between different
manufacturing processes. Not all specialty products are
differentiated. For example, pharmaceutical products like
aspirin (acetylsalicylic acid) are undifferentiated. Different
manufacturers can produce aspirin and there is nothing to
choose between these products, other than the price and
differentiation created through marketing of the product.
Scale of production also differs between the three classes
of chemical products. Fine and specialty chemicals tend
to be produced in volumes less than 1000 t·y−1 . On the
other hand, commodity chemicals tend to be produced in
much larger volumes than this. However, the distinction
is again not so clear. Polymers are differentiated products
because they are purchased on the basis of their mechanical
properties, but can be produced in quantities significantly
higher than 1000 t·y−1 .
When a new chemical product is first developed, it
can often be protected by a patent in the early years of
commercial exploitation. For a product to be eligible to
be patented, it must be novel, useful and unobvious. If
patent protection can be obtained, this effectively gives
the producer a monopoly for commercial exploitation of
the product until the patent expires. Patent protection lasts
for 20 years from the filing date of the patent. Once the
patent expires, competitors can join in and manufacture the
product. If competitors cannot wait until the patent expires,
then alternative competing products must be developed.
Another way to protect a competitive edge for a new
product is to protect it by secrecy. The formula for CocaCola has been kept a secret for over 100 years. Potentially,
there is no time limit on such protection. However, for
the protection through secrecy to be viable, competitors
must not be able to reproduce the product from chemical
analysis. This is likely to be the case only for certain classes
of specialty and food products for which the properties of
2
The Nature of Chemical Process Design and Integration
the product depend on both the chemical composition and
the method of manufacture.
Figure 1.1 illustrates different product life cycles 1,2 . The
general trend is that when a new product is introduced
into the market, the sales grow slowly until the market
is established and then more rapidly once the market is
established. If there is patent protection, then competitors
will not be able to exploit the same product commercially
until the patent expires, when competitors can produce the
same product and take market share. It is expected that
competitive products will cause sales to diminish later in
the product life cycle until sales become so low that a
company would be expected to withdraw from the market.
In Figure 1.1, Product A appears to be a poor product that
has a short life with low sales volume. It might be that it
cannot compete well with other competitive products, and
alternative products quickly force the company out of that
business. However, a low sales volume is not the main
criterion to withdraw from the market. It might be that
a product with low volume finds a market niche and can
be sold for a high value. On the other hand, if it were
competing with other products with similar functions in
the same market sector, which keeps both the sale price
and volume low, then it would seem wise to withdraw
from the market. Product B in Figure 1.1 appears to be
a better product, showing a longer life cycle and higher
sales volume. This has patent protection but sales decrease
rapidly after patent protection is lost, leading to loss of
market through competition. Product C in Figure 1.1 is
a still better product. This shows high sales volume with
the life of the product extended through reformulation of
the product1 . Finally, Product D in Figure 1.1 shows a
product life cycle that is typical of commodity chemicals.
Commodity chemicals tend not to exhibit the same kind
of life cycles as fine and specialty chemicals. In the early
years of the commercial exploitation, the sales volume
grows rapidly to a high volume, but then does not decline
and enters a mature period of slow growth, or, in some
exceptional cases, slow decline. This is because commodity
chemicals tend to have a diverse range of uses. Even though
competition might take away some end uses, new end uses
are introduced, leading to an extended life cycle.
The different classes of chemical products will have
very different added value (the difference between the
selling price of the product and the purchase cost of
raw materials). Commodity chemicals tend to have low
added value, whereas fine and specialty chemicals tend to
have high added value. Commodity chemicals tend to be
produced in large volumes with low added value, while
fine and specialty chemicals tend to be produced in small
volumes with high added value.
Because of this, when designing a process for a
commodity chemical, it is usually important to keep
operating costs as low as possible. The capital cost of the
process will tend to be high relative to a process for fine or
specialty chemicals because of the scale of production.
When designing a process for specialty chemicals,
priority tends to be given to the product, rather than to
the process. This is because the unique function of th